Diffusion of electromagnetic fields into the earth from a line source of current

Geophysics ◽  
1982 ◽  
Vol 47 (11) ◽  
pp. 1585-1592 ◽  
Author(s):  
M. L. Oristaglio
Keyword(s):  
Half Space ◽  
Line Source ◽  
Scattering Problems ◽  
The Earth ◽  
Steady Current ◽  
Transient Solutions ◽  
Em Induction ◽  
Time Domain Electromagnetic ◽  
Full Solution ◽  
Smoke Ring

The popularity of time‐domain electromagnetic (EM) systems in geophysical exploration has stimulated much interest in transient solutions of Maxwell’s equations. Although the fields at the surface of the earth are of the most practical value, the patterns of current flow in the ground can also be very enlightening, as demonstrated by Nabighian (1979) who showed the development and diffusion of the now famous “smoke ring” of current in the earth after shut‐off of a steady current in a loop at the surface. Nabighian’s result, which is based on Weaver’s (1970) general theory of EM induction in a half‐space, is an approximate image solution involving a single current filament; however, calculation of the full solution by numerical integration of the appropriate Hankel transforms showed that the real currents in the earth follow a similar smoke‐ring pattern (Nabighian, 1979; Lewis and Lee, 1978). Since the two‐dimensional (2-D) approximation is often used in solving EM scattering problems, it is interesting to consider the currents generated by a line source at the surface of a half‐space.

Influence of displacement currents on the response of helicopter electromagnetic systems

Geophysics ◽  
2005 ◽  
Vol 70 (4) ◽  
pp. G95-G100 ◽  
Author(s):  
Changchun Yin ◽  
Greg Hodges
Keyword(s):  
Phase Shift ◽  
Dielectric Permittivity ◽  
Half Space ◽  
Free Space ◽  
Phase Changes ◽  
Displacement Current ◽  
Speed Of Light ◽  
Finite Speed ◽  
The Earth ◽  
Full Solution

For the purpose of shallow-earth geophysical mapping, progressively higher frequencies have been developed for helicopter electromagnetic (HEM) systems. However, concern has been expressed about the vulnerability of high-frequency EM signals to the influence of the displacement current, especially the phase shift of the HEM signal resulting from the finite speed of light that describes the propagation of the EM wave in free space. In this paper we investigate the influence of the displacement current and the finite speed of light on HEM responses, based on a full solution of the EM field for a conductive, magnetically, and dielectrically polarizable earth half-space and an overlying half-space of air with free-space dielectric permittivity. We calculate the amplitude change and the phase shift of the HEM signal and the change in the apparent resistivity. We find that the displacement current, when both the air and the earth half-space assume the free-space dielectric permittivity, has a small influence on the HEM signal, while substantial influence may occur when the earth is dielectrically polarizable. The finite speed of the EM propagation in free space does not result in significant phase changes in the HEM signal.

scholarly journals Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems

2021 ◽  
Author(s):  
Changkun Wei ◽  
Jiaqing Yang ◽  
Bo Zhang
Keyword(s):  
Time Domain ◽  
Electromagnetic Scattering ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Scattering Problems ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Time Domain Electromagnetic ◽  
Numer Anal ◽  
The Time Domain

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{\infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).

Transient electromagnetic fields of a buried horizontal magnetic dipole

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. E481-E491 ◽  
Author(s):  
Andrei Swidinsky ◽  
Misac Nabighian
Keyword(s):  
Electric Field ◽  
Magnetic Dipole ◽  
Time Domain ◽  
Major Axis ◽  
Secondary Response ◽  
Burial Depth ◽  
Transient Electromagnetic ◽  
The Earth ◽  
Smoke Ring ◽  
Electromagnetic Surveys

Electromagnetic surveys using a vertical transmitter loop are common in land, marine, and airborne geophysical exploration. Most of these horizontal magnetic dipole (HMD) systems operate in the frequency domain, measuring the time derivative of the induced magnetic fields, and therefore a majority of studies have focused on this subset of field measurements. We examine the time-domain electromagnetic response of a HMD including the electric fields and corresponding smoke rings produced in a conductive half-space. Cases of a dipole at the surface and buried within the earth are considered. Results indicate that when the current in the transmitter is rapidly switched off, a single smoke ring is produced within the plane of the vertical transmitter loop, which is then distorted by the air-earth interface. In this situation, the circular smoke ring, which would normally diffuse symmetrically away from the source in a whole space, is approximately transformed into an ellipse, with a vertical major axis at an early time and a horizontal major axis at a late time. As measured from the location of the transmitter, the depth of investigation and lateral footprint of such a system increases with burial depth. It is also observed that the electric field measured in the direction of the magnetic dipole only contains a secondary response related to the charge accumulation on any horizontal conductivity boundaries because the primary field is always absent. This field component can be expressed analytically in terms of a static and time-varying field, the latter term adding spatial complexity to the total horizontal electric field at the earth surface at early times. Applications of this theoretical study include the design of time-domain induction-logging tools, crossborehole electromagnetic surveys, underground mine expansion work, mine rescue procedures, and novel marine electromagnetic experiments.

Effect of a Moving Dielectric Half-Space on the Radiation From a Line Source

Radio Science ◽  
1969 ◽  
Vol 4 (5) ◽  
pp. 483-488 ◽  
Author(s):  
K. Hazama ◽  
T. Shiozawa ◽  
I. Kawano
Keyword(s):  
Half Space ◽  
Line Source
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